Constraint-Embedded Fractal Self-Similar Generation of Synthetic Topologies for Receiving-End Power Grids with Rich Renewable Energy: A Hybrid Metaheuristic Approach
- 1Key Laboratory of Power System Intelligent Dispatch and Control of Ministry of Education, Shandong University, Jinan 250061, China
- 2State Grid Economic and Technological Research Institute Co., Ltd., Changping District, Beijing 102209, China
- 3National Key Laboratory of Power Grid Security, China Electric Power Research Institute Co., Ltd., Haidian District, Beijing 100192, China
Abstract
Fractal geometry offers a natural language for the self-similarity and scale invariance of power networks, yet future receiving-end grids shaped by high renewable penetration, high load density and large HVDC infeed have no historical counterpart. This paper formalizes the synthesis of such grids as a Constrained Fractal Iteration System (CFIS), in which synthetic topology is generated by the scale-progressive composition of three fractal operators, each coupling a spatial clustering/topology operator with an engineering constraint-projection operator. A hybrid metaheuristic realizes the operators through dynamic-weighted K-means (DWK-Means), social-learning particle swarm optimization (SL-PSO) and constraint-embedded 2-opt (CE-2-opt). On a provincial receiving-end grid at 162, 234, and 363 GW, the generated topologies are scale-invariant over a well-defined box-size range: the box-counting dimension rises from 1.675 to 1.800 with load and shows a clear voltage-layered hierarchy; the constrained dimension remains within 1.5% of the unconstrained value, showing that engineering feasibility costs almost no fractal quality. The 500 kV station set attains a correlation dimension of 1.81 versus 1.69 for the real existing grid, consistent with the interpretation of the synthetic grid as an idealized fractal upper bound. Short-circuit levels are brought within the 63 kA limit after correction, and renewable curtailment and load shedding remain zero; N-1 screening of all elements shows that the worst post-contingency loading falls from 98.5% at 162 GW to 91.4% at 363 GW, satisfying the thermal limits under single contingencies. Against classical topology generators built on the same node set, the proposed backbone attains full degree-two redundancy and a comparable fractal dimension with about 24% less line length, and an ablation of the redundancy bound shows that it, rather than the short-circuit limit, governs steady-state security at the low load scale.
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BibTeX
@article{yu2026constraintembedded,
title = {{Constraint-Embedded Fractal Self-Similar Generation of Synthetic Topologies for Receiving-End Power Grids with Rich Renewable Energy: A Hybrid Metaheuristic Approach}},
author = {Yue Yu and Yifei Pan and Changgang Li and Shuolin Zhang and Jingyi Zhang and Yan Zhang and Libo Zhang},
journal = {Fractal and Fractional},
year = {2026},
month = oct,
doi = {10.3390/fractalfract10110756},
url = {https://www.mdpi.com/2504-3110/10/11/756},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Constraint-Embedded Fractal Self-Similar Generation of Synthetic Topologies for Receiving-End Power Grids with Rich Renewable Energy: A Hybrid Metaheuristic Approach
AU - Yue Yu
AU - Yifei Pan
AU - Changgang Li
AU - Shuolin Zhang
AU - Jingyi Zhang
AU - Yan Zhang
AU - Libo Zhang
PY - 2026
DA - 2026/10/29
JO - Fractal and Fractional
DO - 10.3390/fractalfract10110756
UR - https://www.mdpi.com/2504-3110/10/11/756
AB - Fractal geometry offers a natural language for the self-similarity and scale invariance of power networks, yet future receiving-end grids shaped by high renewable penetration, high load density and large HVDC infeed have no historical counterpart. This paper formalizes the synthesis of such grids as a Constrained Fractal Iteration System (CFIS), in which synthetic topology is generated by the scale-progressive composition of three fractal operators, each coupling a spatial clustering/topology operator with an engineering constraint-projection operator. A hybrid metaheuristic realizes the operators through dynamic-weighted K-means (DWK-Means), social-learning particle swarm optimization (SL-PSO) and constraint-embedded 2-opt (CE-2-opt). On a provincial receiving-end grid at 162, 234, and 363 GW, the generated topologies are scale-invariant over a well-defined box-size range: the box-counting dimension rises from 1.675 to 1.800 with load and shows a clear voltage-layered hierarchy; the constrained dimension remains within 1.5% of the unconstrained value, showing that engineering feasibility costs almost no fractal quality. The 500 kV station set attains a correlation dimension of 1.81 versus 1.69 for the real existing grid, consistent with the interpretation of the synthetic grid as an idealized fractal upper bound. Short-circuit levels are brought within the 63 kA limit after correction, and renewable curtailment and load shedding remain zero; N-1 screening of all elements shows that the worst post-contingency loading falls from 98.5% at 162 GW to 91.4% at 363 GW, satisfying the thermal limits under single contingencies. Against classical topology generators built on the same node set, the proposed backbone attains full degree-two redundancy and a comparable fractal dimension with about 24% less line length, and an ablation of the redundancy bound shows that it, rather than the short-circuit limit, governs steady-state security at the low load scale.
SN - 2504-3110
ER -